Marxism is a political praxis and social theory based on the works of Karl Marx, a nineteenth century philosopher, economist, journalist, and revolutionary. Marx drew on Hegel's philosophy, the political economy of Adam Smith, Ricardian economics, and 19th century French socialism to develop a critique of society which he claimed was both scientific and revolutionary. This critique achieved its most systematic (if unfinished) expression in his chef d'oeuvre[?], Capital: A Critique of Political Economy (Das Kapital).

It is important to note that there have been many conflicting interpretations and definitions of Marxism. A year before his death, Marx remarked to his son-in-law, Paul Lafargue, "What is certain is that I am no Marxist!"

It is by no means certain that Marx's work does form an organic whole. Although his basic analytic method was consistent, he developed new conclusions as he applied it to new material. Moreover, he died before finishing Capital.

Since Marx's death in 1883, various revolutionaries[?] around the world have appealed to Marxism as the intellectual basis for their politics and policies, which can be dramatically different and conflicting. Although there are still many Marxist revolutionary movements[?] and political parties around the world, relatively few countries have Marxist governments in power. Cuba, North Korea, and China have governments in power which describe themselves as Marxist.

Hegel proposed a form of idealism in which ideas gradually developed in history. Marx retained Hegel's emphasis on history, but stood Hegel on his head in proposing that material circumstances shape ideas, instead of the other way around.
Marx summarizes his material theory of history, otherwise known as historical materialism, in A Contribution to the Critique of Political Economy:

In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness.

Marx emphasized that the development of material life will come into conflict with the superstructure. These contradictions, he thought, were the driving force of history. Marx illustrated his ideas most prominently by the development of capitalism from feudalism and by the prediction of the development of socialism from capitalism.

Political economy is essential to this vision, and Marx built on and critiqued the most well-known economists of his day, the British classical economists. Marx followed Adam Smith and David Ricardo in claiming that the source of profits under capitalism is value added by workers not paid out in wages. He developed this theory of exploitation of the proletariat with an exposition of the labor theory of value in the first volume of Capital, while remaining aware that the labor theory of value was not a valid theory of relative prices. He critiqued Smith and Ricardo, on the other hand, for not realizing their economic concepts reflected capitalist institutions, not innate natural properties of mankind, and could not be applied unchanged to all societies. Marx's theories of business cycles; of economic growth and development, especially in two sector models; and of the declining rate of profit are other important elements of Marxist economics.

the working class or proletariat: Marx defined this class as "those individuals who sell their labor and do not own the means of production" whom he believed were responsible for creating the wealth of a society (buildings, bridges and furniture, for example, are physically built by members of this class). The proletariat may be further subdivided into the ordinary proletariat and the lumpenproletariat, those who are extremely poor and cannot find legal work on a regular basis. These may be prostitutes, beggars, or homeless people.

the bourgeoisie : those who "own the means of production" and employ the proletariat. The bourgeoisie may be further subdivided into the very wealthy bourgeoisie and the petty bourgeoisie: those who employ labor, but also work themselves. These may be small proprietors, land-holding peasants, or trade workers.

Marx developed these ideas to support his advocacy of socialism and communism: "The philosophers have only interpreted the world differently; the point is, to change it." Communism would be a social form wherein this system would have been ended and the working classes would be the sole beneficiary of the "fruits of their labour".

Socialists often (or, in varying degrees) do not recognize an individual right to private property. At any rate, socialist philosophers have argued that there is not a specific right to private property, though it might be in the best interest of society in general for certain individuals to have exclusive control over certain goods, so long as this control does not lead to the class divisions and exploitation of the working class they seek to eliminate. Critics have said that "socialism is a system in which everyone is equally poor", arguing that because individuals are not rewarded more on the basis of supply and demand, there is less incentive for individual achievement, improving technology, and other factors that result in a higher standard of living.

Some of these ideas were shared by anarchists, though they differed in their beliefs on how to bring about an end to the class society. Socialist thinkers suggested that the working class should take over the existing capitalist state, turning it into a workers revolutionary state, which would put in place the democratic structures necessary, and then "wither away". On the anarchist side people such as Mikhail Bakunin and Peter Kropotkin argued that the state per se was the problem, and that destroying it should be the aim of any revolutionary activity.

Many governments, political parties, social movements, and academic theorists have claimed to be founded on Marxist principles. Social democratic movements in 20th century Europe, the Soviet Union and other Eastern bloc countries, Mao and other revolutionaries in agrarian developing countries are particularly important examples. These struggles have added new ideas to Marx and otherwise transmuted Marxism so much that it is difficult to specify its core.

It is usual to speak of Marxian theory when referring to political study that draws of the work of Marx for the analysis and understanding of existing (usually capitalist) economies, but rejects the the more speculative predictions that Marx and many of his followers made about post-capitalist societies.

The 1917 October Revolution, led by Vladimir Lenin and Leon Trotsky was the first large scale attempt to put Marxist ideas about a workers' state into practice. However, counterrevolution, civil war, foreign interventions and the failure of a socialist revolution in Germany and in the other western countries gave Joseph Stalin the opportunity to take over power when Lenin died. As predicted by Lenin, Trotsky and others already in the 1920's, Stalin's "socialism in one country" was unable to maintain itself, and the USSR ceased to show the characteristics of a socialist state long before its formal dissolution.